Voskresenskaya, G. V. Cusp forms and finite subgroups in \(SL(5, \mathbb{C})\). (English. Russian original) Zbl 0847.11022 Funct. Anal. Appl. 29, No. 2, 129-130 (1995); translation from Funkts. Anal. Prilozh. 29, No. 2, 71-73 (1995). This is an announcement of results concerning the following problem: Find a finite group such that all 28 multiplicative eta-products can be associated with elements of this group by means of some representation. It is known [G. Mason, Math. Ann. 283, 381-409 (1989; Zbl 0636.10021)] that 21 of these eta-products are associated with the Mathieu group \(M_{24}\). The author claims that all multiplicative eta-products with weight \(> 1\) can be associated with finite order elements of \(\text{SL}(5, \mathbb{C})\). Reviewer: G.Köhler (Würzburg) Cited in 1 ReviewCited in 6 Documents MSC: 11F20 Dedekind eta function, Dedekind sums 11F11 Holomorphic modular forms of integral weight 11F22 Relationship to Lie algebras and finite simple groups Keywords:cusp forms; finite subgroups; multiplicative eta-products; Mathieu group Citations:Zbl 0636.10021 PDF BibTeX XML Cite \textit{G. V. Voskresenskaya}, Funct. Anal. Appl. 29, No. 2, 129--130 (1995; Zbl 0847.11022); translation from Funkts. Anal. Prilozh. 29, No. 2, 71--73 (1995) Full Text: DOI OpenURL References: [1] G. Mason, Contemp. Math.,45, 223-244 (1985). [2] G. Mason, Math. Ann.,283, 381-409 (1989). · Zbl 0636.10021 [3] D. Dummit, H. Kisilevsky, and J. McKay, Contemp. Math.,45, 89-98 (1985). [4] M. Koike, Nagoya Math. J.,95, 85-89 (1984). [5] G. V. Voskresenskaya, Mat. Zametki,52, No. 1, 25-31 (1992). This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.